Grade 6 Math · Topic 32

Prime and Composite Numbers

A whole number greater than 1 is prime if its only factors are 1 and itself. If it has any other factor, it is composite. The number 1 is special — it is neither prime nor composite.

Lesson alignment: 6.NS.B.4 · Take your time. You can return to this lesson whenever you need it.

Explore visually

Find the factor pairs

A prime number has only one whole-number array: 1 row by the number of tiles.

Think first: How many factor-pair arrays do you expect besides 1 × the number?

Ready? Reveal the model and try your prediction

Swipe horizontally to see the full diagram.

Turn on JavaScript to adjust this model. The examples and practice below work without it.

Follow the worked examples

Read each step, then cover the explanation and see if you can explain why it works.

Worked example 1

Is 29 prime or composite?

Check primes up to √29 ≈ 5.4, so try 2, 3, 5. 29 is odd (∤ 2), digit sum 11 (∤ 3), doesn't end in 0 or 5 (∤ 5). 29 is prime.

Answer: Prime

Worked example 2

Is 51 prime or composite?

Start by writing the calculation clearly: 51 = 3 × 17. Since it has factors other than 1 and 51, it is composite.

Answer: Composite

Try a few on your own

Work these on paper first. Open “Check” when you are ready to compare your answer.

  1. 7 ⇒
    Check

    P

  2. 15 ⇒
    Check

    C

  3. 23 ⇒
    Check

    P

  4. 39 ⇒
    Check

    C

  5. 41 ⇒
    Check

    P

  6. 57 ⇒
    Check

    C

  7. 71 ⇒
    Check

    P

  8. 91 ⇒
    Check

    C

Try this situation 1

A teacher wants to arrange 17 students into equal-sized groups (more than one group, more than one student per group). Is this possible?

Show a worked solution

Answer: No.

Start by writing the calculation clearly: 17 is prime, so its only factors are 1 and 17. No other equal-group arrangement is possible.

Try this situation 2

Is 111 prime? Justify your answer.

Show a worked solution

Answer: No — it is composite.

Digit sum 1+1+1 = 3, so 111 ÷ 3 = 37. Thus 111 = 3 × 37.

Fresh questions · saved on this device

Practice this skill

11 question pool

Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.

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Check what you learned

Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.

1. Jamal factors several numbers and records his work: 32 = 2⁵, 25 = 5², 17 = prime, 48 = 2⁴ × 3. How many of these numbers are composite?

2. Carmen lists the factors of 36. Her list is: 1, 2, 3, 4, 6, 9, 12, 18, 36. Based on this, which statement is correct?

3. Which of the following numbers is prime?

4. Which list contains only prime numbers?

5. Which of these numbers is prime?

Practice and finish

Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.

Open the practice quiz

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More Grade 6 resources

Use these free materials if you want another explanation, extra paper practice, or a broader review.

Browse free Grade 6 topic lessons ↗Print Grade 6 worksheets ↗Review Grade 6 flashcards ↗Open the formula review ↗Try the Factors, Multiples & Percents quiz ↗Try a full practice test ↗